can I render some elements the way they look in material preview and how to do it?
First, you can do it in the 3D Viewport only. Find a View menu, and click the Viewport Render Animation. It will render the animation right from the viewport, using EEVEE if in solid or material preview mode. If you disable screen overlays, you can easily get nice renders in EEVEE this way, however, this is limited and inaccurate (not enough screen samples will be used, and softshadows can be blurry and flickering, among other limitations).

Here is the place where you can find View menu:


And then, find this menu command: